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This article is cited in 4 scientific papers (total in 4 papers)
On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis
N. F. Abuzyarova Bashkir State University, Ufa
Abstract:
In the work we consider a topological module $\mathcal P(a;b)$ of entire functions, which is the isomorphic image of the Schwarz space of distributions with compact supports in a finite or infinite interval $(a;b)\subset\mathbb R$ under the Fourier–Laplace transform. We prove that each weakly localizable module in $\mathcal P (a;b)$ is either generated by its two elements or is equal to the closure of two submodules of special form. We also provide dual results on subspaces in $C^\infty(a;b)$ invariant w.r.t. the differentiation operator.
Keywords:
entire functions, subharmonic functions, Fourier–Laplace transform, finitely generated submodules, description of submodules, local description of submodules, invariant subspaces, spectral synthesis.
Received: 31.05.2016
Citation:
N. F. Abuzyarova, “On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufimsk. Mat. Zh., 8:3 (2016), 8–21; Ufa Math. J., 8:3 (2016), 8–21
Linking options:
https://www.mathnet.ru/eng/ufa322https://doi.org/10.13108/2016-8-3-8 https://www.mathnet.ru/eng/ufa/v8/i3/p8
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Abstract page: | 254 | Russian version PDF: | 91 | English version PDF: | 10 | References: | 45 |
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